Bob and Will toss two coins. If both coins come up heads, Bob pays Will $6. Will pays Bob $2 otherwise. What is the expected value of this game for Bob?
A)$0.25
B)$0.50
C)$0.00
D)$4.00

Question

Quizplus · Accepted Answer

The expected value for Bob is calculated by considering all possible outcomes of the coin tosses. There are four possible outcomes: HH, HT, TH, TT. The probability of getting both heads (HH) is 1/4, and the probability of any other outcome (HT, TH, TT) is 3/4. If both coins come up heads, Bob pays Will $6, so the expected value for this outcome is -6 * 1/4 = -$1.50. For any other outcome, Will pays Bob $2, so the expected value for these outcomes is 2 * 3/4 = $1.50. Adding these together, -$1.50 + $1.50 = $0.00, which means the expected value of the game for Bob is $0.00.

Bob and Will Toss Two Coins